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5
votes
MATLAB loops are slow. This is known. If you use something like C++ or Julia you'll get much closer (like 5x-10x or so IIRC). So that's why it's super crazy. Still, the algorithms that MATLAB is call …
answered Jan 18 '18 by Chris Rackauckas
3
votes
Using the interpolation to come up with an error estimate of the continuous (dense) solution is known as residual control. This is done quite frequently when the Runge-Kutta methods are utilized for d …
answered Sep 2 '18 by Chris Rackauckas
2
votes
MATLAB's ODE solvers can use what are known as Event functions to achieve this. I also link someone who posted a good quick example to show how to use it that is close to your use-case.
answered Apr 26 '16 by Chris Rackauckas
6
votes
No. Different discretizations are stable/unstable on different PDEs. There is no one size fits all approach to the whole class of PDEs. (Even for ODEs there are generic methods but which methods are …
answered Aug 13 '18 by Chris Rackauckas
2
votes
Take a classic paper like this one from Davie and Gaines on solving the stochastic heat equation. By equation (2) they say We consider finite-difference approximations to (1). The simplest such a …
answered Jul 4 by Chris Rackauckas
4
votes
This seems to be in common for most schemes, as the Butcher tableau for the implicit part has only nonzero elements in the first column. However, this does not seem like an implicit treatment. What …
answered Feb 19 '18 by Chris Rackauckas
1
vote
Ignoring Newton's method here is the wrong approach! The fact that you're using Newton's method is what makes this cheap to add, and is what makes singular mass matrices possible. Essentially look at …
answered Mar 3 by Chris Rackauckas
6
votes
First of all, don't even consider "optimizing" before you're using the right integration method. Chucking more computers at the problem may sound like the easiest way to solve it, but in reality it wi …
answered May 25 '18 by Chris Rackauckas